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Diffusion amid random overlapping obstacles: Similarities invariants approximations

机译:随机重叠障碍物之间的扩散:相似性不变量近似值

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摘要

Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (Deff) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (ϕ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of Deff (ϕ) for obstacles of any given shape. In 3D, the similarities of effective diffusion yield a simple multiplication “rule” that provides a fast means of estimating Deff for a mixture of overlapping obstacles of different shapes with comparable sizes.
机译:高效,准确的数值技术用于检查随机重叠障碍物之间的空隙中有效扩散的相似性:有效扩散系数(Deff)关于障碍物形状的基本不变性以及两参数幂定律在几乎整个排除范围内的适用性体积分数(ϕ),只有很小的渗透阈值附近。结果表明,虽然这两个属性都不是精确的,但与它们的偏差却很小。这允许快速估计空隙渗透阈值,并近似重建任何给定形状的障碍物的Deff(ϕ)。在3D中,有效扩散的相似性产生了一个简单的乘法“规则”,它为估计具有相似大小的不同形状的重叠障碍物的混合物提供了一种估算Deff的快速方法。

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